1. Field of the Invention
This invention is related to methods for correcting well log data for the effects of changes in the velocity of a logging instrument as it moves along a wellbore. The changes in velocity are primarily caused by a phenomenon known in the art as cable "yo-yo". The invention is particularly related to data processing methods for well logging instruments which produce output by combining measurements made at more than one depth within the wellbore.
2. Description of the Related Art
Electric wireline well logging instruments are typically inserted into and withdrawn from wellbores by means of armored electrical cables. The logging instruments generate signals which are related to physical properties of the earth formations through which the wellbore is drilled. A record of the properties of the earth formations with respect to depth in the wellbore is generally made at the earth's surface by pulling the logging instrument out of the wellbore by reeling the cable onto a winch or similar spooling device, while simultaneously recording the signals generated by the logging instrument. The record of the measurements is thus made to correspond to the apparent depth within the wellbore at which the measurements were made by the logging instruments.
Measurement of the apparent depth of the instrument in the wellbore is typically performed with a calibrated wheel placed in frictional contact with the cable at the earth's surface. The calibrated wheel turns correspondingly with the amount of linear motion of the cable as the cable is moved into or out of the wellbore by the winch. The wheel can be rotationally coupled to a mechanical counter calibrated to indicate the length of cable moved past the wheel, or the wheel can be coupled to an electronic encoder connected to a computer or electronic counter to indicate and record the length of cable which has moved past the wheel. It is assumed that the length of cable extended past the wheel directly corresponds to depth of the instrument in the wellbore.
Calibrated wheels can accurately determine the total length of cable which has been spooled past the wheel into the wellbore, but the true depth of the instrument in the wellbore may not correspond exactly to the spooled length of cable because the cable is subject to change in its overall length as the tension on the cable varies. The tension on the cable is affected by things such as the total weight of the cable disposed within the wellbore, which can be as much as 500 pounds for each 1000 feet of cable. Tension is also affected by the weight of the instrument when it is inserted into the wellbore, which weight can vary depending on instrument density (related to the weight of the instrument and how much of the instrument volume is enclosed air space) and the density of a fluid ("drilling mud" or "completion fluid") which may fill the wellbore, and can also be affected by friction caused by movement of the instrument against the wall of the wellbore.
Friction is the least predictable of the causes of tension on the cable as it is moved into and out of the wellbore because the wall surface of the wellbore has an indeterminate degree of roughness and the earth formations penetrated by the wellbore have indeterminate frictional coefficients. The fluid which typically fills the wellbore can have indeterminate viscosity and lubricating properties at different depths within a particular wellbore, making determination of friction even more difficult.
It is frequently the case that the measurements made by the instrument can have been made at depths as much as ten feet or more different from the depth caused to be indicated by the calibrated wheel because of tension induced stretch in the cable. Various methods have been developed to correct the apparent depth measurements for changes in the stretch of the cable as caused by the previously described factors. U. S. Pat. No. 3,490,149 issued to Bowers, for example, describes using measurements made by accelerometers disposed in the logging instrument to calculate a change in axial position of the logging instrument, so that the cable length measurements made at the earth's surface can be corrected by using the calculated change in instrument position. U. S. Pat. No. 4,545,242 issued to Chan describes a more sophisticated method for using accelerometer measurements to determine a "correct" instrument position. U. S. Pat. No. 5,541,587 issued to Priest describes a method for determining correct depth of a well logging instrument using a combination of accelerometer measurements and a measurement of phase shift in an electrical signal passed through the logging cable, where the phase shift corresponds directly to the overall length of the logging cable. The phase shift measurement thus corresponds to the amount of stretch in the cable, this measurement being used to calculate instrument position where the accelerometer measurements are least effective and most erroneous, namely when the acceleration on the instrument is zero.
The effectiveness of the prior art methods for correcting cable length measurements to reflect correct depth, however, depends on the fact that most prior art logging instruments provide a calculated output representative of a selected formation property for each depth (axial) position in the wellbore using only measurements acquired by the instrument at that same axial position. At the earth's surface, a record of instrument signals is made with respect to depth, as previously explained. For the typical well logging instrument known in the art, a calculated output is generated at each of the recorded depth levels by processing measurements made by the instrument only at that same depth. While it may be undesirable to have small residual errors in the depth measurement, particularly for instruments which make very finely detailed (in the axial direction) measurements such as the "imaging" instrument described in the Chan '242 patent, for example, typically any small-scale residual errors in the depth measurement do not adversely affect the accuracy of the measurement made by logging instruments which are used to generate calculated output only at depths corresponding to the recording depth of the input data. Therefore, even if the absolute depth value corresponding to the measurement made by these logging instruments is somewhat imprecise, the value of the measurements themselves will properly reflect the value of the formation property in the formation which was adjacent to instrument at the moment of data recording.
More recently, certain types of logging instruments have been developed which use measurements made at more than one depth in the wellbore to generate a calculated output corresponding to a property of the earth formation at a single depth in the wellbore. One example of such an instrument is known as a "long-spaced" acoustic logging instrument, shown in FIG. 1A at A. The long-spaced acoustic logging instrument A includes two or more acoustic transmitters T1, T2 at one end of the instrument A, and a pair or an array of acoustic receivers R1, R2 on the other end of the instrument A. Differences in acoustic travel time between one of the transmitters T1 and each of the receivers R1, R2 are recorded when the receivers R1, R2 are adjacent to a formation of interest F. Similarly, differences in acoustic travel time are recorded after the instrument A has moved so that two of the transmitters T1, T2 are adjacent to the formation of interest F, as shown in FIG. 1B. The acoustic travel times are typically measured between one of the receivers R1 at the other end of the instrument and the two transmitters T1, T2. The two sets of travel time measurements, first made with the instrument A positioned as shown in FIG. 1A, and those measured with the instrument A positioned as shown in FIG. 1B, are then averaged to provide a "borehole compensated" measurement of acoustic interval travel time (generally inverted into acoustic velocity) within the formation of interest F. The method of calculating the borehole compensated velocity depends on having the transmitters T1, T2 in FIG. 1B positioned adjacent to exactly the same interval of formation (the formation of interest F) as were the receivers R1, R2 in FIG. 1A in the previous set of measurements. The typical long-spaced acoustic logging instrument has transmitter to receiver spacings such that the instrument is moved about 8 to 12 feet between the two sets of measurements. Errors in depth measurement between the two sets of measurements can result in significant error in the calculated result where even only very small errors in depth measurement occur.
While the example of the acoustic logging instrument serves to illustrate the mechanics of the problem caused by residual depth measurement error, the residual depth error problem has not generally been found to cause objectionable error in the calculated results from most types of well logging measurements. More recently, however, certain types of well logging instruments have been developed for which even very small residual errors in the depth measurement cause large error in some of the calculated results. One such instrument is described in a paper by X. Li et al entitled, "High-Definition Lateral Log and its Application to the Study of Formation Resistivity", Paper "N", The Fourth Well Logging Symposium of Japan, Sep. 24-25, 1998. The instrument described in the X. Li et al paper makes measurements of voltage, voltage difference and second difference of voltages between axially spaced apart electrodes along an insulated sonde mandrel. In order to process the measurements into a representation of resistivity (the representation known in the art as "focused" resistivity) of the formations of interest, it is necessary to have various ones of the electrodes positioned adjacent to the exact same formation of interest. Even very small errors in positioning of the instrument have shown to provide unacceptable calculated results. None of the prior art methods for correcting depth measurement have proven adequate to overcome the errors in the calculated results for these logging instruments.